Problem: The grades on a language midterm at Gardner Bullis are normally distributed with $\mu = 83$ and $\sigma = 3.5$. Gabriela earned a n $82$ on the exam. Find the z-score for Gabriela's exam grade. Round to two decimal places.
Explanation: A z-score is defined as the number of standard deviations a specific point is away from the mean We can calculate the z-score for Gabriela's exam grade by subtracting the mean $(\mu)$ from her grade and then dividing by the standard deviation $(\sigma)$ $ { z = \dfrac{x - {\mu}}{{\sigma}}} $ $ { z = \dfrac{82 - {83}}{{3.5}}} $ ${ z \approx -0.29}$ The z-score is $-0.29$. In other words, Gabriela's score was $0.29$ standard deviations below the mean.